Systems and methods for grid forming control

Control strategies for grid-connected power converters can be broadly categorized into grid-forming and grid-following controls. Grid-following control assumes that the grid frequency and voltage magnitude are stable and change slowly and controls the converter as a current/power source relative to the stable grid. Grid-forming control uses power converters to imposes a stable voltage waveform (e.g., frequency and magnitude) at the point of connection and contributes to grid stability. However, by imposing the terminal voltage, grid-forming converters are vulnerable to overcurrent due to grid faults. Existing methods for current limiting of grid-forming converters can, at best, successfully limit the fault current during a balanced fault, but not during unbalanced faults or with severely unbalanced loads. Existing grid-forming control, which provides a voltage reference to the power converter or its inner controls, is limited to providing a balanced voltage reference.

Accordingly, improved systems, methods, and media for improved grid-forming control are desirable.

In accordance with some embodiments of the disclosed subject matter, systems, methods, and media for grid forming control are provided.

According to some aspects of the present disclosure, a grid forming control system for a power converter having a plurality of phases is provided. The system can include a phasor determination unit configured to, for each of the plurality of phases, receive a frequency reference for the phase and determine voltage and current phasors as well as an active power and a reactive power for the phase based on an electrical measurement for the phase and the frequency reference for the phase, a GFM controller configured to, for each of the plurality of phases, determine the frequency reference for the phase based on the active power for the phase and balancing feedback across the plurality of phases and determine a voltage magnitude reference for the phase based on the reactive power for the phase and balancing feedback across the plurality of phases, and a control loop configured to, for each of the plurality of phases, determine a control signal for the power converter based on the determined voltage magnitude reference for the phase.

According to some aspects of the present disclosure, a method for controlling a power converter (e.g., voltage source converter) having a plurality of phases is provided. The method can include, for each of the plurality of phases: receiving a frequency reference for the phase, determining an active power and a reactive power for the phase based on an electrical measurement for the phase and the frequency reference for the phase, determining a voltage magnitude reference for the phase based on the reactive power for the phase and balancing feedback across the plurality of phases, determining the frequency reference for the phase based on the active power for the phase and balancing feedback across the plurality of phases, and determining a control signal for the power converter based on the determined voltage magnitude reference for the phase.

In accordance with some embodiments of the disclosed subject matter, systems, methods, and media for a grid forming controller are provided. In particular, novel systems and methods are introduced to solve unbalanced fault ride-through challenges, with a fault response that can reliably trip standard protective devices. Advantageously, systems and methods according to various embodiments of the present disclosure may provide an unbalanced voltage during an unbalanced fault or severely unbalanced load to control its current injection. Systems and methods according to various embodiments may maintain sinusoidal current and voltage waveforms with no or minimal distortion during a fault and after clearing the fault.

A grid-forming (GFM) converter according to various aspects of the present disclosure may comprise a grid-forming control (GFM control) and a multi-phase power converter, such as a voltage source converter (VSC) or current source inverter, treated as separate individual single-phase power converters. In some embodiments, the power converter may comprise a VSC and each single-phase VSC may have its own grid-forming control (e.g., droop control) with underlying single-phase current and voltage control loops. The VSC may take an input power, such as a direct current (DC) power and modulate it to an output alternating current (AC) waveform based on a modulated voltage reference from the grid-forming control. This allows full control over all degrees of freedom in the appropriate coordinates (e.g., phase quantities) and eliminates delays associated with estimating sequence components. The grid-forming controls may further comprise a phase-balancing feedback configured to synchronize and/or balance the three individual single-phase grid-forming controls when possible, and enable a controlled trade-off between current/power unbalance and voltage unbalance during unbalanced faults or when feeding severely unbalanced load(s). The GFM voltage magnitude references may be tracked by individual inner current and/or voltage controllers for every phase with current limiting. A GFM converter according to the present disclosure may maintain control over the VSC terminal voltage under unbalanced conditions and phase current under unbalanced faults. While the present disclosure exemplifies embodiments for controlling a VSC, other power converter topologies (such as current source inverters) may be controlled as will be described below.

1 FIG. 1 FIG. 100 100 102 112 108 100 112 102 108 112 104 106 112 104 106 100 130 110 114 102 104 140 106 illustrates a multi-phase, for example a three-phase, GFM convertersystem according to various aspects of the present disclosure. In some embodiments, the GFM convertermay comprise, for each phase p∈(e.g.,defined as {a, b, c} for three phases a, b, and c), a GFM controller, a control loop, and a multi-phase VSChaving the same number of phases as the overall GFM converter(e.g., three phases). In some embodiments, the control loopfor a phase may be configured to receive a voltage magnitude reference from the GFM controllerfor that phase, and determine a modulated voltage reference for that phase to be provided to the VSC. In some embodiments, the control loopmay comprise a voltage controller(e.g., configured as an outer control loop), and a current controller(e.g., configured as an inner control loop). The gains of the inner and outer loops may be coordinated and chosen relative to the network circuit dynamics to ensure performance and stability. In some embodiments, the control loopmay comprise a current limiter between the voltage controllerand current controller. The GFM convertermay further comprise a phasor determination unit, a filter, and a power transformer.representatively illustrates, as an exemplary embodiment, a GFM controller, voltage controller, current limiter, and current controllerfor each of the multiple phases, and specifically labels these and their respective inputs and output for a first phase “a”.

100 104 140 106 In some embodiments, the GFM convertermay comprise a current source inverter instead of a voltage source converter. The current source inverter may control the output AC waveform based on a current reference. In such embodiments, the current source inverter may receive the current reference from the voltage controller(e.g., if current limiting is not implemented) or the output of the current limiter, without a need for the current controller.

130 108 110 130 130 130 130 102 The phasor determination unitmay comprise any suitable system or method configured to determine the quadrature components of the electrical signals of each of the phases at the output of the VSCand/or filter. The phasor determination unitmay receive instantaneous multi-phase signals (e.g., electrical measurements) and determine respective phasors and a complex power for each phase. The phasor determination unitmay receive phase currents and voltages (e.g., measured by the phasor determination unitor external to the phasor determination unit), and phase frequency references from the GFM controller, and may determine the quadrature components of the phase currents and voltages at the respective frequency references. Each measured value (phase current or voltage) and its determined quadrature component represent a current or voltage phasor at the given frequency.

130 108 108 110 124 122 130 110 130 102 130 102 130 130 130 100 106 104 130 p p o,p p p p p p p In some embodiments, the phasor determination unitmay receive, for each phase, the measured filter current (i) output by the VSCand the measured terminal voltage (v) (e.g., at the output of the VSCor filter(e.g., across a capacitorof the filter)). In some embodiments, the phasor determination unitmay optionally also receive, for each phase, the measured output current (i) output by the filter. The phasor determination unitmay further receive, for reach phase, a frequency reference (ω) from the GFM controller. In some embodiments, the phasor determination unitmay optionally also receive, for each phase, a voltage phase angle reference (θ) from the GFM controller. The phasor determination unitmay implement a phasor estimation algorithm that uses the received electrical signals of every phase and the frequency reference to estimate the quadrature components of the electrical signals of every phase. In some embodiments, the phasor determination unitmay use the voltage phase angle reference (θ) to align the coordinate frame with the respective rotating vector. The phasor determination unitmay provide the determined quadrature components along with the respective measured values (e.g., as voltage or current phasors (represented as upper case I and V herein)) to various components of the GFM converter, for example a current phasor to the current controllerand a voltage phasor to the voltage controller. In some embodiments, the phasor determination unitmay provide per-phase determined active power (P) and reactive power (Q) (or, for example, a complex power (S)).

2 FIG.A 130 130 210 220 210 p o,p p p Referring to, the phasor determination unitmay comprise any suitable system or method for determining the quadrature (orthogonal) component of the received input signals (e.g., input i, i, v). As noted above, in some embodiments the phasor determination unitmay use the voltage phase angle reference (θ) to align the coordinate frame, whereas in some alternative embodiments it need not be so aligned. In some embodiments, the phasor determination unit may comprise a phasor determination portionand a power measurement portion. In some embodiments, the phasor determination portionmay implement a Hilbert transform, for example according to:

p p o,p p where xrepresents the respective per-phase voltage or current measurement (e.g., i, i, v), and

p p 2 FIG.B 210  represents its respective orthogonal component. Under the assumption that x(t) is a sinusoid with slowly changing frequency ω(t), the time shifting in Eq. 1 approximates a 90 degree phase shift. In some alternative embodiments, briefly referring to, the phasor determination portionmay be configured as a state observer, for example according to:

240 p wherein an estimatorperforms the respective matrix calculation to determine {circumflex over (x)}and

p 102 220 100 210 L is the observer gain, and ωis again the per-phase frequency reference provided by the GFM controller. The observer gain L may be determined using standard methods, such as pole placement or LQR-type approaches. The method for determining the quadrature component according to Eq. 1 provides the component values without modification, whereas the state observer (e.g., according to Eq. 2) provides the components as filtered values. The power measurement portion(as well as other respective components of the GFM converter) may be configured to accept the component values with or without modification (e.g., filtered or unfiltered components) depending on the phasor determination portionimplementation.

p p p p In some embodiments, an AC signal x(t) (such as i, v, etc.) can be represented in a dq frame with reference angle θ(t) as:

where R is the 2D rotation matrix. The phasor can then be constructed as:

2 FIG.A 220 210 220 p p p p As noted above, upper-case variables may be used herein to refer to phasor quantities, but it will be understood that the use of phasor quantities may be interchangeable with the equivalent representations in the dq frame or the equivalent time-domain AC signal and its orthogonal component. Referring again to, the power measurement portionmay receive the determined current and voltage phasors (e.g., I, V, or the respective components thereof (whether or not modified as discussed above)) from the phasor determination portionand may determine the per-phase active power (P) and reactive power (Q). For example, in some embodiments the power measurement portionmay determine the respective average power values over one cycle according to:

p o,p where i(t) may generally be interchangeable with i(t).

130 230 p In some embodiments, the phasor determination unitmay include a filter portion, for example implementing a double line frequency notch filter to remove error in the estimation. The filter may have a center frequency of 2ω. For example, if implemented using a processing unit, the processing unit may run at a sampling rate. Therefore the time shift in the Hilbert transform cannot be implemented with infinite time resolution and may not be able to perform the time shift to the required accuracy. Moreover, performing the Hilbert transform may take a non-zero amount of time, so the required time shift may fall a little before or after a sampling period. Both of these aspects may lead to errors that the notch filter may alleviate.

1 FIG. 1 FIG. 102 102 Referring again to, the GFM controllersmay receive the phasors or estimates of the phase powers (e.g., active and reactive power, represented as S in) obtained from the phasors for every electrical signal for each phase, and each GFM controllermay provide a voltage magnitude reference

104 130 102 108 130 102 102 p to the respective voltage controllerand a frequency reference (ω) to the phasor determination unit. In some embodiments, the GFM controllersmay comprise any suitable system or method for determining a voltage magnitude reference and frequency reference for a phase based at least partially on phase quantities of the current and voltage output by the VSC(for example received from the phasor determination unit) as well as a balancing feedback. In some embodiments, the multiple GFM controllers(one for each phase) may be implemented by a single GFM controller configured to determine the respective per-phase values. In some embodiments, the GFM controllermay implement so-called droop control.

102 As noted above, the GFM controllermay implement a balancing feedback to configurably balance voltage magnitude and angles across the phases (e.g., a voltage magnitude balancing feedback and an angle balancing feedback, respectively) based on desired tradeoffs. In some embodiments, the balancing feedback may be implemented with an active power droop control and reactive power droop control, for example according to (in per unit):

gfm p Q s s o where Vare the voltage magnitude references for the phases, δ are the deviations of the voltage phase angle reference from a balanced synchronous solution for each phase, mand mare the droop gains, kis the phase balancing gain and controls the tradeoff between voltage and power unbalance (e.g., larger kresults in more balanced voltage),represents the set of phases (as discussed above), the subscript lower-case “p” refers to the phase being evaluated (e.g., phase a, b, or c), τ is a lowpass filter time constant, ωis the nominal frequency, V* is the voltage setpoint, and

3 FIG.A 300 are the active and reactive power setpoints (respectively). Eq. 6 representatively illustrates an exemplary angle balancing feedback, and Eq. 7 representatively illustrates an exemplary voltage magnitude balancing feedback.illustrates an exemplary embodiment of an active power droop controllerimplementing Eq. 6 using hardware and/or software components. The quantity

3 FIG.A 3 FIG.B p 310 from Eq. 6 is represented inby ΔPfor each of the respective phases.illustrates an exemplary embodiment of a reactive power droop controllerimplementing Eq. 7 using hardware and/or software components.

102 100 P Q s s s The balancing feedback may synchronize all individual GFM controllers, for example ensuring that their voltage magnitudes are identical and phase angles are shifted by the appropriate amount when possible (e.g. phase angles shifted by 120 degrees for a three-phase GFM converter), and otherwise trading off voltage and power unbalance. In some embodiments, the variables mand mmay be provided by a system operator, t may be small and generally fixed, and kmay be application-dependent (e.g., distribution, transmission, etc.) but tunable as described above. For example, in a distribution system setting one may simulate predetermined test cases, taking into consideration load unbalance and equipment requirements (e.g., induction motor requirements), and increase kuntil the voltage unbalance remains under a given threshold. In a transmission system setting, simulations of unbalanced faults may be used to decrease kto improve, e.g., the critical clearing time by allowing increased voltage unbalance during unbalanced faults.

p The frequency reference (ω) may be determined according to:

where the quantities

3 FIG.A p  may be taken, for example, from just prior to the integration blocks (“1/s”) in. The voltage phase angle reference (θ) may be determined according to:

where

for a three-phase system.

102 Accordingly, the GFM controllersmay determine voltage magnitude references (e.g.,

a b c p 102 112 104 130 112 102 130 112 and frequency references (e.g., ω, ω, ω) according to Eqs. 6-8 above. The GFM controllermay output the voltage magnitude references to the control loop(e.g., to voltage controllers), and the frequency references to the phasor determination unit. In some embodiments, for example when the control loopis configured to operate on an aligned reference frame, the GFM controllersmay determine the voltage phase angle references θaccording to Eq. 9 above and may provide them to the phasor determination unit. In some embodiments, the control loopmay be configured to operate without an aligned reference frame and the voltage phase angle reference need not be determined.

112 104 104 112 In some embodiments, the control loopmay comprise a voltage controllerfor each phase. The voltage controllermay comprise any suitable system or method for determining the difference (e.g., error) between a voltage magnitude reference for a phase and a measured voltage for the phase, and accordingly determining a current reference. Therefore, the control loopmay determine multiple current references (e.g.,

104 104 104 p one from each voltage controller. Current reference determination may be performed by any suitable system or method. In some embodiments, the voltage controllermay comprise a proportional integral (PI) controller, for example in a dq frame relative to the GFM voltage phase angle reference θ, configured to determine the current reference based on the determined error. In some embodiments, the voltage controllermay comprise a proportional resonant (PR) controller, proportional integral derivative (PID) controller, or the like.

104 In some embodiments, the voltage controllermay comprise a PI controller and the current reference may be determined according to:

where

PI f 110 are the current references, G(s) is the PI controller function, Yis the filter admittance matrix (i.e., based on the filter), and voltage reference

112 140 140 In some embodiments, the control loopmay comprise a current limiterfor each phase. Current limiting may be implemented with any suitable system or method. In some embodiments, the current limitermay be configured to receive the current references

and determine current-limited references

106 max for input to the current controller, for example by scaling the current reference vector down if its magnitude is too large. According to some embodiments, if current limiting is applied to phase a (e.g., during a phase a to ground fault), then current limiting may dominate (e.g., over the balancing feedback) for phase a, while the balancing feedback continues to control phases b and c. For further example, current limiting may be performed using instantaneous saturation limits, vector amplitude limitation/latched limits, virtual impedance, virtual admittance, or the like. In some embodiments according to the present disclosure, the current-limited references may be based on the maximum phase current magnitude I, for example according to:

140 Notably, a current limiteraccording to Eq. 11 will not clip the current waveform, and instead adjusts the magnitude of the sinusoidal reference current for every phase to avoid introducing harmonics into the system.

112 106 106 108 112 106 106 106 sw,a sw,b sw,c p In some embodiments, for example when the power converter is a VSC, the control loopmay comprise a current controllerfor each phase. The current controllermay comprise any suitable system or method for determining the difference (e.g., error) between a current reference for a phase and a measured current for the phase, and accordingly determining a modulated voltage reference for the VSC. Therefore, the control loopmay determine multiple modulated voltage references (e.g., v, v, v), one from each current controller. Modulated voltage reference determination may be performed by any suitable system or method. In some embodiments, the current controllermay comprise a proportional integral (PI) controller in a dq frame relative to the GFM voltage phase angle reference θconfigured to determine the modulated voltage reference based on the determined error. In some embodiments, the current controllermay comprise a proportional resonant (PR) controller, proportional integral derivative (PID) controller, or the like.

106 In some embodiments, the current controllermay comprise a PI controller and the modulated voltage reference may be determined according to:

sw,p f 110 where vare the modulated voltage references and Zis the filter impedance matrix (i.e., based on the filter). In some embodiments, the modulated voltage references may be determined based on the current references

instead of the current-limited references

for example when no current limiting is implemented.

108 100 108 108 106 108 108 108 100 sw,a sw,b sw,c In some embodiments, the VSCmay comprise any suitable system or method for converting an input power to an output AC voltage waveform for each phase of the GFM converter. The VSCmay be configured to receive power from any suitable power source (not shown), such as renewable generation (e.g., solar PV), energy storage (e.g., batteries), and the like. The VSCmay be configured to determine the AC voltage waveform for each phase based upon the received modulated voltage references from the current controllers(e.g., v, v, v). The VSCmay convert the received modulated voltage references into appropriate control signals. For example, in the case of a two-level DC/AC voltage source converter, the VSCmay convert the modulated voltage references to appropriate pulse width modulated signals. For further example, in the case of a modular multi-level converter, the VSCmay convert the modulated voltage references using nearest level or optimized switching frequency modulation. In addition, as mentioned above, if the GFM converteruses a current source inverter instead of a voltage source converter, the current source inverter may be controlled from the current-limited reference

108 When the midpoint of the DC side of the VSCis grounded, the phase-to-ground voltages can be controlled on the AC side as described above. If the midpoint of the DC side is not grounded, phase-to-phase voltages of two “virtual” phases (instead of three physical phases) may be controlled by implementing the control described above in αβ coordinates using a Clarke transform (e.g., synchronize to a phase difference of 90 degrees instead of 120 degrees, and the setwould contain two entries instead of three).

108 110 110 114 110 114 116 114 In some embodiments, the VSCmay output the AC voltage waveform to the filter. The filtermay provide the filtered phase waveforms to the power transformer. The filtermay be configured to remove switching harmonics. In some embodiments, the filter may be used in delta or wye configuration based on the grounding of the DC side and tradeoffs between voltage magnitude and fault ride through on the AC side. The power transformermay comprise any suitable transformer configurable to connect to an external power grid. In some embodiments, the power transformermay comprise a wye or delta configuration. In some transmission systems, a wye-connected filter, delt-wye-ground transformer with grounding on the grid side may be used to achieve a path for fault current. In some microgrids and distribution systems, delta-connected filters may be used with no transformer (or an inductor in place of the transformer to increase coupling impedance to the network) to increase the voltage magnitude on the AC side.

4 FIG. 100 400 100 400 100 400 400 100 400 410 400 Referring to, various components of the GFM convertermay be implemented on one or more controllers. In some embodiments, all phases of the GFM converterare implemented using the same controller. In some embodiments, the control for each phase of the GFM convertermay be implemented using separate controllers. The controllermay be configured to send and/or receive information (e.g., including instructions, data, values, signals, or the like) to/from the various components of the GFM converter. The controllermay comprise processing circuitry, for example, a processor, DSP, CPU, APU, GPU, microcontroller, application-specific integrated circuit, programmable gate array, and the like, any other digital and/or analog components, as well as combinations of the foregoing (whether distributed, networked, locally connected, or the like), and may further comprise inputs and outputs for receiving and providing control instructions, control signals, drive signals, power signals, sensor signals (e.g., current or voltage sensor output), digital signals, analog signals, and the like. All such computing devices and environments are intended to fall within the meaning of the term “controller,” “control unit,” “processor,” “processing device,” or “processing circuitry” as used herein unless a different meaning is explicitly provided or otherwise clear from the context. In some examples, the controllermay comprise one or more such processor devices.

400 410 430 420 420 420 420 400 102 104 106 140 108 130 100 430 The controllermay comprise processing circuitryconfigured to execute operating routine(s)stored in a memory. The memorymay include any suitable volatile memory, non-volatile memory, storage, any other suitable type of storage medium, or any suitable combination thereof. For example, the memorymay include RAM, ROM, EEPROM, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, etc. In some embodiments, the memorymay have encoded thereon a computer program (e.g., operating routine) for controlling operation of the controller, GFM controller, voltage controller, current controller, the current limiter, the VSC, the phasor determination unit, and the like. In some embodiments, the various components of the GFM convertermay be implemented entirely as software (e.g., operating routine), entirely as hardware, or any suitable combination thereof. In some embodiments, the operating routine(s)may comprise firmware.

In some implementations, devices or systems disclosed herein can be utilized or configured for operation using methods embodying aspects of the invention. Correspondingly, description herein of particular features, capabilities, or intended purposes of a device or system is generally intended to inherently include disclosure of a method of using such features for the intended purposes, a method implementing such capabilities, and a method of configuring disclosed (or otherwise known) components to support these purposes or capabilities. Similarly, unless otherwise indicated or limited, discussion herein of any method of manufacturing or using a particular device or system, including configuring the device or system for operation, is intended to inherently include disclosure, as embodiments of the invention, of the utilized features and implemented capabilities of such device or system.

112 102 400 Correspondingly, some embodiments of the present disclosure can include a method for providing multi-phase (e.g., three-phase) grid forming control using multiple single-phase grid forming controls and/or single-phase power converters with balancing feedback. In some embodiments, single-phase GFM controls (e.g., control loopand GFM controller) may be implemented on a separate controller (e.g., controller) for each phase, with either a single multi-phase power converter or separate single-phase power converters for each phase. The separate controllers may implement a high sampling rate (e.g., in real-time) for measuring and processing the electric signals, while the balancing feedback may be implemented through communication at a lower rate. For example, a set of buildings (e.g., homes) may collectively receive multiple phases (e.g., three phases) of power with each building receiving one of the phases of power from a single-phase power converter, and each single-phase power converter may be controlled by single-phase GFM controls with balancing feedback performed through a lower-bandwidth communication. For further example, some of the more complex converter topologies (e.g., a modular multilevel converter) may be implemented as a multi-phase power converter consisting of separate power electronic modules for every phase, and communicating electrical measurements and control signals to a centralized controller may result in a high cost. In such cases, the GFM controls may be separated into single-phase GFM control for every separate power electronic module each implementing one phase control using local measurements and implementing balancing feedback through communication, which would require less communication between the individual controllers.

5 FIG. 500 500 400 430 420 500 510 520 530 540 550 Referring to, a non-limiting example of method for grid forming controlis illustrated. In some embodiments, the grid forming control methodmay be implemented in the controller, for example, as operating routinesstored in memory(e.g., as software). The grid forming control methodmay comprise measuring electrical signals of each phase, estimating phase quantities of the measured electrical signals, performing balancing feedback based on the estimated phase quantities, providing a voltage magnitude reference and frequency reference for each phase, and controlling the current and filter voltage for each phase.

510 122 108 120 110 118 108 124 110 520 130 530 102 520 510 p o p p At step, electrical signals of each phase may be measured. In some embodiments, the filter current (i)output by the VSC, the output current (i)of the filter, and the terminal voltage (v)(e.g., at the output of the VSCor across the capacitorof the filter) may be measured. At step, the direct and quadrature components of the current and voltage of each phase may be determined, for example by the phasor determination unit. In some embodiments, the frequency reference ωfrom step(e.g., implemented by the GFM controller) may be used in the phasor estimation. In some embodiments, the quadrature components may be estimated using a Hilbert transform (Eq. 1) or a state observer (Eq. 2). Further, at step, active and reactive power phasors may be determined based on the determined direct and quadrature components of the electrical signals from step, for example according to Eqs. 5a and 5b. In some embodiments, phasor estimation may further include filtering through a double line frequency notch filter to remove error in the estimation.

530 102 530 102 530 100 520 530 At step, balancing feedback may be performed among the multiple phases, for example by a GFM controllerfor each phase. In some embodiments, balancing feedbackmay comprise synchronizing the multiple (e.g., three) grid forming controllers. For example, balancing feedbackmay include ensuring that the voltage magnitude of each phase are identical and phase angles are shifted by the appropriate amount (e.g., 120 degrees for a three-phase GFM converter) when possible and otherwise trading off voltage and power unbalance. In some embodiments, balancing feedback may be performed based on the phasors determined in step. In some embodiments, performing balancing feedbackmay include using Eqs. 6 and 7 (as described above) to configurably balance voltage magnitude and phase angles according to desired tradeoffs. Accordingly, voltage magnitude references (e.g.,

p 530 and frequency references (e.g., ω) may be determined at step.

540 100 540 108 112 540 130 520 At step, the determined voltage magnitude references and frequency references may be provided to the various components of the GFM converter. In some embodiments, at step, the voltage magnitude references may be provided to control the power converter (e.g., the VSC). For example, the voltage magnitude references may be provided, per-phase, to a respective control loopfor that phase, which may determine control signals for the power converter. In some embodiments, at step, the frequency references may be provided to the phasor determination unit, for example to use in stepas described above. The various references may be provided in any suitable manner, for example as digital representations, analog signals, or the like.

550 100 550 100 112 108 550 104 At step, the current and voltage output by the GFM convertermay be controlled. In some embodiments, at step, the current and voltage output by the GFM convertermay be controlled by the respective control loopper phase, for example by providing a control signal to the VSCor a current source inverter. In some embodiments, at step, the received voltage magnitude reference for each phase may be compared to the measured voltage for the phase, and a current reference for each phase determined accordingly, for example according to Eq. 10. In some embodiments, the current references are determined by a voltage controllerfor each phase.

550 140 100 100 In some embodiments, at step, current limiting may be performed on the determined current references, for example by the current limiter. For example, in the case of an unbalanced fault, current limiting may be performed per-phase, for example according to Eq. 11, to limit the current output by the GFM converter. The current reference vector may be re-scaled if its magnitude is too large. In some embodiments, if a first phase is current limited (overriding the balancing feedback for that phase), the remaining phases may still be controlled according to the balancing feedback. In some embodiments, for example when the power converter is a current source inverter, the current-limited reference may be provided to the control the current source inverter and thus the current and voltage output by the GFM converter.

550 106 550 108 100 In some embodiments, at step, for example when the power converter is a voltage source converter, the determined current reference or current-limited reference for each phase may be compared to the measured current for the phase, and a modulated voltage reference for each phase determined accordingly, for example according to Eq. 12. In some embodiments, current limiting may be performed prior to comparing with the measured current. In some embodiments, the modulated voltage references are determined by a current controllerfor each phase. The modulated voltage reference may be provided, at step, to the VSCto control its output, and thus the current and voltage output by the GFM converter.

100 112 108 110 500 510 500 As described above, the voltage and current output by the GFM convertermay be output according to the control signal from the control loop, for example by the VSCand through a filter. The grid forming control methodmay then repeat, for example starting with measuring the new electrical signals of each phase. The operating frequency of the grid forming control method may depend on the switch technology and converter topology. In some exemplary embodiments, the grid forming control methodmay operate at about 500 Hz, 1000 Hz, 5,000 Hz, 10,000 Hz, 20,000 Hz, or the like.

6 FIG. 6 FIG. 600 100 102 112 130 108 610 620 640 630 108 P Q Referring to, by way of example, a modelof a three-phase distribution network having a GFM converteraccording to the present disclosure was created and simulated. The GFM control (e.g.,,,(not shown)) controls a two-level DC/AC VSCmodeled as connected to an infinite busthrough a 1 kilometer medium voltage line, a 10 kilometer double circuit high voltage transmission line, and step up transformers. The respective modeled system parameters are shown in, and the GFM control (m=m=5%) is implemented at a sampling rate of 10 kHz. The VSCreceives an input power (not shown), for example from a renewable energy source, and outputs controlled voltages and currents for phases A, B, and C.

650 600 660 100 To illustrate the impact of separate voltage and current control and current limiting for every phase on unbalanced fault ride through, the zero impedance line-to-ground (A-G) faultof the modelcan be activated, which can be cleared by opening the circuit breaker(s)which may happen after ten AC cycles (e.g. at 60 Hz). The GFM convertercan limit current during the fault. If the fault is cleared within the critical clearing time, the system can continue operating as normal.

7 7 FIGS.A-D 7 7 FIGS.A andB 7 7 FIGS.C andD 100 600 650 108 140 106 660 s p p p p max 5 illustrate the response of the GFM converterand the modelto the fault on one line (e.g., the A-G fault) that occurs as 1.5 seconds. Note that due to the transformer connection, the fault applied to phase A of the transmission line is effectively mapped to phase B at the VSCterminal. In this example, k=10.illustrate the magnitude of the terminal voltage Vand filter current Iphasors for each phase, respectively (in per unit). Because the magnitudes of the phase voltages and currents are not well-defined within a cycle, the maximum magnitude over one cycle is shown.illustrate the active power Pand reactive power Qfor each phase, respectively (in per unit). The results show that the current limiterand current controllersuccessfully limit the current magnitude to I=1.2 p.u. within each cycle. By controlling the current phasor for every phase, the GFM control according to the present disclosure manages sub-cycle overcurrent. At approximately 1.675 seconds, the faulted line is cut off (i.e., by circuit breakers). Once the fault is cleared, a resynchronization transient is observed.

100 100 100 630 600 100 One or more GFM convertersaccording to the present disclosure may be used for any given power generation application. For example, on a wind farm, each wind turbine may use one or two GFM converters. An exemplary solar farm may use many GFM converters, with each GFM output coupled to the same transformer (e.g., a transformer as represented by transformersin the model) and each GFM input coupled to solar panels or batteries. In some embodiments, a plurality of parallel transformer may be used, each with several GFMsper transformer.

100 102 100 100 In some applications, only individual phases of a three-phase power supply are used, for example to individual homes or individual floors of a high-rise building. For example, a first floor of a building might receive a first phase, a second floor of a building might receive a second phase, and a third floor of a building might receive a third phase. A GFM converteraccording to the present disclosure may perform balancing feedback (e.g., by GFM controllers) between the first, second, and third floor. Similarly, each of a plurality of houses may receive a single phase from among the three phases. A GFM convertermay perform balancing feedback between single-phase GFM convertersat the houses.

s Systems and methods according to the present disclosure have several advantages. The balancing gain kallows for adjustment of trade-off between phase voltage unbalance and power unbalance at the converter ac terminal, for example allowing to adjust the contribution of a DC/AC VSC to mitigating voltage unbalances in a distribution system. Further, the control described herein tracks voltage references for every phase, and can control and limit the phase currents individually. In addition, the control described herein can addresses sub-cycle overcurrent by continuously estimating and controlling phase current phasors and limiting their magnitude.

It will be appreciated by those skilled in the art that while the disclosed subject matter has been described above in connection with particular embodiments and examples, the present disclosure and the claims of the present disclosure are not necessarily so limited, and that numerous other embodiments, process flows and step ordering, examples, uses, modifications and departures from the embodiments, examples and uses are intended to be encompassed by the claims attached hereto. It will be appreciated that there are additional ways to implement the control methods described herein with different topologies and hardware/software, while using the same signal/phase estimations techniques. The entire disclosure of each patent and publication cited herein is hereby incorporated by reference, as if each such patent or publication were individually incorporated by reference herein.

Various features and advantages of the various aspects presented in the present disclosure are set forth in the following claims.